Transverse and longitudinal waves – problems and solutions

Transverse and longitudinal waves – problems and solutions

1. A wave is traveling down a 3-m long wire for 0.3 seconds. What is the period of the wave?

Known :

Time interval (t) = 0.3 seconds

Wanted : Period (T)

Solution :

1 wavelength = 1 crests + 1 troughs

Period = 2 x 0.1 second = 0.2 seconds

2. The wave speed according to figure below is…

Known :

1 wavelength has 1 crests and 1 troughs. According to figure above, 1 wavelength = 2 meters x 4 = 8 meters.

Periode of wave (T) = 0.5 x 4 = 2 seconds

Wanted : The wave speed (v)

Solution :

The wave speed :

v = s / t = λ / T = 8 meters / 2 seconds = 4 meters/second

3. The distance between point A and B is 30 cm. What is the wave speed according to figure below.

Known :

From A to B, there is ¾ wavelength. If the distance between A and B is 30 cm, then the distance of ¼ wavelength is 30 cm / 3 = 10 cm. Thus, 1 wavelength = 4 x 10 cm = 40 cm.

According to the figure above, a period of the wave is 4 seconds.

Wanted : The wave speed (v)

Solution :

v = d / t = λ / t

v = the wave speed, d = distance, λ = wavelength, t = time interval

The wave speed :

v = λ / t = 40 cm / 4 seconds = 10 cm / 1 second = 10 cm/second

4. If the distance of A and B = 250 cm, then the wave speed is…

Known :

Distance of A and B = 5/4 wavelength = 250 cm.

1/4 wavelength = 250 cm / 5 = 50 cm

1 wavelength = 4/4 wavelength = 4 x 50 cm = 200 cm

Period (T) = 2 seconds

Wanted : The wave speed

Solution :

Formula of the wave speed :

v = d / t = λ / t

v = the wave speed, d = distance λ = wavelength, t = time interval

The wave speed :

v = 200 cm / 2 seconds = 100 cm/second

5. Amplitude of wave are shown by….

Solution :

The amplitude of the wave is BB’ and DD”.

1. What distinguishes a transverse wave from a longitudinal wave in terms of particle motion?
   • Answer: In a transverse wave, particles of the medium move perpendicular to the direction of the wave propagation. In a longitudinal wave, particles move parallel to the direction of wave propagation.
2. Provide a common example of a transverse wave and a longitudinal wave.
   • Answer: A common example of a transverse wave is a wave on a string or water waves. A common example of a longitudinal wave is a sound wave in air.
3. Can solids support both transverse and longitudinal waves?
   • Answer: Yes, solids can support both transverse and longitudinal waves. However, fluids (gases and liquids) typically only support longitudinal waves.
4. How does compression and rarefaction relate to longitudinal waves?
   • Answer: In longitudinal waves, compression refers to the region where particles of the medium are closest together, and rarefaction refers to the region where particles are furthest apart. These regions correspond to the crests and troughs in transverse waves.
5. Why can we hear sound (a longitudinal wave) around corners but not see light (which behaves as a transverse wave) in the same manner?
   • Answer: Sound can diffract, or spread out, around obstacles more noticeably than light due to its longer wavelength compared to visible light. While both sound and light exhibit diffraction, the shorter wavelengths of visible light mean that its diffraction effects are less pronounced in everyday scenarios.
6. How do the velocities of transverse and longitudinal waves in the same medium compare?
   • Answer: The velocities of transverse and longitudinal waves in the same medium can be different. For instance, in solids, the speed of a longitudinal (P-wave) is typically faster than that of a transverse (S-wave).
7. Can a medium exhibit both transverse and longitudinal wave motion simultaneously?
   • Answer: Yes, certain disturbances can produce both transverse and longitudinal waves in a medium simultaneously. For example, earthquakes produce both P-waves (longitudinal) and S-waves (transverse) that travel through the Earth.
8. Which type of wave would be more likely to produce a polarized effect upon propagation?
   • Answer: Transverse waves can be polarized. Polarization involves the restriction of vibrations to a single plane. Longitudinal waves, due to their back-and-forth motion, cannot be polarized in this manner.
9. What kind of wave is an electromagnetic wave, like light or radio waves?
   • Answer: Electromagnetic waves are transverse waves. Their electric and magnetic fields oscillate perpendicular to the direction of wave propagation.
10. Why are S-waves (a type of transverse wave) not observed to travel through the Earth’s outer core during earthquakes?

• Answer: S-waves do not travel through the Earth’s outer core because it is believed to be liquid. Transverse waves require a medium that can support shear stresses, which solids can, but fluids (liquids and gases) cannot.